Two points $A$ and $B$ are situated at a distance $x$ and $2x$ respectively from the nearer pole of a magnet $2\,cm$ long. The ratio of magnetic field at $A$ and $B$ is

A closely wound solenoid of $800$ turns and area of cross section $2.5 \times 10^{-4} \;m ^{2}$ carries a current of $3.0\; A .$ Explain the sense in which the solenoid acts like a bar magnet. What is its associated magnetic moment?

The ultimate individual unit of magnetism in any magnet is called

Assume the dipole model for earth’s magnetic field $\mathrm{B}$ which is given by

${{\rm{B}}_{\rm{v}}} = $ vertical component of magnetic field

$ = \frac{{{\mu _0}}}{{4\pi }}\frac{{2m\,\cos \theta }}{{{r^3}}}$

${{\rm{B}}_H} = $ Horizontal component of magnetic field

${{\rm{B}}_H} = \frac{{{\mu _0}}}{{4\pi }}\frac{{m\,\sin \theta }}{{{r^3}}}$

$\theta $ $= 90^{°}$ -latitude as measured from magnetic equator.

$(a)$ Find loci of points for which : $\left| {{\rm{\vec B}}} \right|$ is minimum;

Write a brief history of magnet.

Two magnetic dipoles $X$ and $Y$ are placed at a separation $d$, with their axes perpendicular to each other. The dipole moment of $Y$ is twice that of $X$. A particle of charge $q$ is passing through their mid-point $P$, at angle $\theta  = 45^o$ with the horizontal line as shown in the figure. What would be the magnitude of force on the particle at that instant ? ($d$ is much larger than the dimensions of the dipole)